It is self-executing. It has the same enforcement mechanism as the part in Article II which states that only people who are over the age of 35 can hold the office of President.
And it's not "Blue state" reasoning. The reason this all came up was because of the paper The Sweep and Force of Section Three, written by two Federalist Society (way way way conservative) guys. It's long, but it's in relatively clear language.
Let's see how you decide to dodge ask number four:
Can you show me which part of the 14th amendment, section three, requires a conviction of any kind?